Question

You are provided with the following information on four stocks. Assume that the base year is Dec 2010 and all splits take place on this date. That is after close of trading on December 31, 2010. Stock A and B have a 2 for 1 split at the end of trading on December 31, 2010. Use this information to answer the questions listed below.

	31-Dec-10	31-Dec-10	31-Dec-11	31-Dec-11	31-Dec-10	Dec-11	Split
Stock	Price	Shares	Price	Shares	MV	MV
A	$ 150.00	10,000	$ 50.00	20,000	$1,500,000	$1,000,000	2
B	$ 50.00	4,000	$ 35.00	8,000	$200,000	$280,000	2
C	$ 25.00	15,000	$ 30.00	15,000	$375,000	$450,000	1
D	$ 140.00	20,000	$ 130.00	20,000	$2,800,000	$2,600,000	1

1. Calculate the rate of return on a price weighted average of the four stocks for the period December 31, 2010 to December 31, 2011. Remember to adjust for changes in the divisor.
2. Calculate the rate of return on a market value weighted index of the four stocks for the period December 31, 2010 to December 31, 2011.
3. Calculate the rate of return on an equally weighted index of the four stocks for the period December 31, 2010 to December 31,2011.

Answer 1

a) Rate of return based on price weighted average

In this rate of return based on prices, total price of all stocks is divided by number of stocks to find out average price and then return calculated over previous period.

Stock	Price as on 31st Dec 2010	Price as on 31st Dec 2011	Return
Stock A	150	50	-67%
Stock B	50	35	-30%
Stock C	25	30	20%
Stock D	140	130	-7%
Total	365	245	-33%
Average price & Rate of return	91.25	61.25	-33%

b) Rate of return based on Market Value

In this method, rate of return is based on Market value of Stocks as on different period and then return calculated over previous period.

Stock	MV as on 31st Dec 2010	MV as on 31st Dec 2010	Return
Stock A	1,500,000	1,000,000	-33%
Stock B	200,000	280,000	40%
Stock C	375,000	450,000	20%
Stock D	2,800,000	2,600,000	-7%
Total Market Value Index	4,875,000	4,330,000
Index Return			-11%

c) Rate of return based on equal weighted index

In equal weighted index Rate of return is simple arithmetical average of all returns.

Stock	Price as on 31st Dec 2010	Price as on 31st Dec 2011	Return
Stock A	150	50	-67%
Stock B	50	35	-30%
Stock C	25	30	20%
Stock D	140	130	-7%
Rate of Return			-84%